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Gough wishes to save some money for a trip to Antarctica. He plans to make regular...

Gough wishes to save some money for a trip to Antarctica. He plans to make regular payments of $1,000 per month for the next 3 years into an account at Mawson Mutual Bank that earns 7% interest per annum compounded half-yearly. The first payment will be made immediately. The future value of Gough’s savings one month after the last payment will be

a. $38,269.51

b. $40,099.47

c. $41,158.77

d. $39,856.49

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Answer #1

The correct answer is option b

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The future value of the savings is found using future value of annuity due equation.

In this example, the payment frequency and compounding frequency are not same. The payment is made monthly but the compounding is done half yearly. Thus we have to adjust for the interest by finding the monthly interest rate.

The monthly interest rate is found as follows

Interest rate per month = 0.575%

Future value savings = $ 40099.47

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